This problem was contributed to the Feynman Lectures Website by Sukumar Chandra.

A hemispherical smooth bowl is held
fixed with its axis vertical. A particle of mass 90gm. attached to one end of a
light inextensible string is placed inside the bowl. The string passes over the
frictionless rim of the bowl and is attached to another 15gm. mass hanging
freely in air at its other end. In equilibrium position of the system of
particles find the angle θ subtended by the radius through the 90gm. particle
with the vertical.

Answer:
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